Accelerating electromagnetic system

The circles between the magnets indicate a wire with current flowing in the direction given. This picture is a cross section of a loop of wire, looking down. Not included in this picture is the battery and non-conductive connecting materials linking the magnets and wire together.

Since the current in the wire goes through a magnetic field, it should experience a force in the direction given by the right hand rule. If the magnets and wire are held together, then it seems that the entire system should accelerate as long as the current keeps on flowing.

This seems like a bizarre conclusion, but I can't think of any way to disprove this conclusion.

Staff: Mentor

It will not. The force is from the device back onto itself. Since it isn't exerting a force on anything not part of itself, and it isn't ejecting any mass as propellent, it will not accelerate. It's like connecting a magnet to the end of a stick and holding in front of a wagon, you aren't going to accelerate.

It will not. The force is from the device back onto itself. Since it isn't exerting a force on anything not part of itself, and it isn't ejecting any mass as propellent, it will not accelerate. It's like connecting a magnet to the end of a stick and holding in front of a wagon, you aren't going to accelerate.

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The electromagnetic field can be used to transfer momentum. Could this explain what is happening here?

For example, a solar sail uses momentum from photons (electromagnetic disturbances) to accelerate.

Could this be what is happening here?

Edit: Also what is the source of the force that counteracts the force on the wire? Where is it felt?

There is a force upward on the wire, but there is also a force downward on the magnets. If you imagine the magnetic field lines created by the current in the wire, they are forcing the magnets downward.

Edit: it is an example of equal and opposite forces, as Drakkith was implying.

No, a solar sail works because the Sun has already emitted the light. The recoil from emission is felt on the Sun, and the photons transfer momentum into the sail through absorption and reflection.

On the magnets. The coil feels a force in one direction, and the magnets feel the force in the opposite direction. They cancel out.

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Could you explain the origin of the force back on the magnets in more detail? The wire feels a force due to the Lorentz Force. I've never seen anything saying that the Lorentz force causing an equal but opposite force back on the origin of the magnetic field.

Thanks!

Edit: I would also like to point out that this construction is somewhat similar to a simple electric motor.

Newton's third law is just another way of saying that momentum is conserved. The crux of the matter is then how momentum is conserved with the Lorentz force. All explanations regarding the conservation of momentum seem to say that the electromagnetic field carries the momentum. The magnets do not receive any of this momentum...

Staff: Mentor

Then where is the momentum for the coil coming from? It's got to come from somewhere, it can't just appear. The EM field can transfer momentum but it cannot create it.
Per the third law, the coils feel a force due to the magnetic field of the magnets. In turn the magnets feel a force from the magnetic field of the coil in the opposite direction.

Edit: Whoops, momentum of course can be created, but it is conserved. Not sure what I was thinking here.

Then where is the momentum for the coil coming from? It's got to come from somewhere, it can't just appear. The EM field can transfer momentum but it cannot create it.
Per the third law, the coils feel a force due to the magnetic field of the magnets. In turn the magnets feel a force from the magnetic field of the coil in the opposite direction.

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There is no change in total momentum. The system gets some momentum, the electromagnetic field gets some momentum, and everybody is happy and Newton's third law is satisfied.

In response to your first two sentences: where does the momentum from an exploding bomb "come from"?

It is totally possible that some instrument gives off EM energy, which causes the instrument to be accelerated, as you have said. And yes, this doesn't disobey any laws. But specific to the picture you drew in the first post, there is a force up on the wire and down on the magnets. You mentioned that your picture is similar to a simple electric motor. This is true. And in a simple electric motor, you can have a fixed magnet and a spinning wire, or you can have a fixed wire with a spinning magnet. This is because there is a force on the magnet too.

That is the electrostatic force, static being the key word here. It implicitly assumes an action at a distance (i.e., infinitely fast) kind of force and it is not a complete description of the electromagnetic interactions when the particles are in motion.

Newton's Third Law can fail in a number of cases:

There is a time delay in the equations of motion, such as is the case for electrodynamics (as opposed to electrostatics). What is happening here is that the field that mediates the interaction is itself storing momentum. There is no room for such in Newton's 3rd. As mentioned before, this can be reconciled by observing that momentum is still conserved. Newton's 3rd law is conservation of momentum in the special case that forces are instantaneous and central in nature.

The force is not central in nature, which once again is the case for electrodynamics. In the strong form of Newton's third law, third law force pairs must be equal but opposite in nature and the force must be directed along or against the line connecting the pair of particle. This form of Newton's third law conserves both translational and angular momentum. Translational and angular momentum can still be conserved in the case of non-central forces if the mediating field stores these momenta, but Newton's third does not apply in such cases.

The underlying interaction inherently involves three or more particles. Newton's third demands that forces be resolvable down to pairs of particles. There are some multi-body interactions in quantum mechanics where the interactions only appears when three or more particles are present. These interactions cannot be isolated down to pairs, and once again Newton's third law fails.

In more advanced physics, it is the conservation laws that reign supreme. Newton's third law derives from the conservation laws with the assumption that forces act in pairs, act instantaneously, and act along the line connecting particle pairs. Drop those assumptions and you have to drop Newton's third law. You do not have to drop the conservation laws, however. In even higher level physics, the conservation laws themselves can be derived from the very nature of space and time.

The current in the wire creates a magnetic field. This magnetic field causes a force on the magnet.

If you imagine the magnetic field lines from the wire and the magnetic field lines from the magnet, you can see what direction is the force on the wire and on the magnet. (a general quick and easy rule of thumb is that the magnetic field lines like to be as uniform as possible).

for example, on the lower part of your picture, the current is going into the page, so in the space just above the 'north' pole, the magnetic field lines from the magnet are going against the field lines created by the wire. And in the space just below the north pole, the field lines are almost matching up. Therefore, this magnet will be pushed downwards, so that the field lines will become less steeply curved.

Another way to work it out is if we give our magnets a specific form. For example, the magnets might be made of solenoids. In this case, you can work out the Lorentz force on the charged particles in the wire of the solenoid, and you can work out the force on the 'magnet' (i.e. solenoid), which gives the same answer as the other method.